Byron Henry is a Lt. Commander and only Commanders and Captains have the scrambled eggs on their cap visors. Admirals have larger.
The American soldiers who discover Natalie are wearing First Army shoulder patches, rather that the divisional patches that front-line troops would be wearing. As well, they're seen carrying various models of British Lee-Enfield rifles rather than American M-1 Rifles or carbines.
Steven Berkoff's eye color is gray-green and it is generally accepted fact that Hitler's eyes were a piercing blue; although those who were closest to him say they were blue-violet.
While Byron is looking for his son in episode 12, and in uniform, he is wearing the shoulder board insignia of a Lt. Commander (04), while also wearing a cap with "scrambled eggs" on the bill. These "eggs" are reserved for Naval officers above the rank of Commander (05).
In the establishing shot of the White House, when President Harry S. Truman gives his address on V-E Day in 1945, a modern bus is seen in the background.
A British officer addresses Byron as "Lieutenant," pronouncing it "lyoo-tenant." He should be pronouncing it "lef-tenant."